In some known winding systems for a web of material, such as paper, the web is wound into a roll. In some systems, the web is perforated at predetermined intervals to form “sheets” such that the sheets may be separated from the roll at a later time. Additionally, in at least some known winding systems, the web of material has a topography that includes a pattern, such as a ripple pattern, that includes indentations and/or embossments that affect a density of the roll as the web is wound. More specifically, a first web having a first pattern may wind into a roll that has a lower density than a second web having a second pattern, when all other parameters, such as tension on each of the two webs, are equal.
In some known winding systems, parameters for controlling winding of a web into a roll are pre-calculated based on a mathematical model. The mathematical model incorporates assumptions regarding the compression of sheets of the roll as the roll is wound. Once the roll is completely wound, aspects such as the density, compressibility, number of sheets in the roll, and diameter of the roll are measured. Based on such measurements, the assumptions are adjusted, and the mathematical model is revised.
Typical through roll variability that occurs during the winding of a roll cannot be accounted for by examining rolls after they are wound. In particular, measuring a finished roll does not provide direct information about factors affecting the density, compressibility, and diameter as the roll is being wound. Importantly, such factors may vary as the roll is being wound. Accordingly, known winding systems do not provide information on how such factors change during the winding of the roll and, as a result, may lead to extended trial and error as assumptions are adjusted and the mathematical model is iteratively revised to achieve target characteristics for a roll.